Liu, Congzheng and Letchford, Adam and Svetunkov, Ivan
(2023)
*Extensions to Newsvendor Problems.*
PhD thesis, Lancaster University.

## Abstract

Newsvendor problems (NVPs) form an important and much-studied family of inventory control problems. Although the use of the term varies somewhat, in most situations the term NVP refers to a single-period stochastic inventory control problem involving a single product. Assuming that the demand comes from a known probability distribution, this classic problem can be solved easily with calculus (Arrow et al., 1951), and the solution appears in nearly all inventory management textbooks. In this thesis, we expand the literature in four directions. In Chapter 2, we consider an integrated approach, in which the NVP order quantities are determined directly from the data. Though the topic of integrated approaches has already been studied in the literature, the idea of constructing a robust approach that deals with nonlinear NVPs is novel. In this chapter, we introduce such an approach, and we perform extensive simulation experiments to examine the performance of the approach in different settings, including situations when the true model is known and when the underlying model is mis-specified. In Chapter 3, we consider the effect that small changes in NVP parameters would have on the optimal solution, which is commonly referred to as sensitivity analysis. We show that one can perform sensitivity analysis for NVP using techniques from stochastic programming and discrete approximation. Our method is very general and can handle changes in prices and costs, changes in demand distributions, and cross-price elasticities of demand. Moreover, computational results show that our method yields accurate estimates with very reasonable computing effort. In Chapter 4, we examine the effect of judgemental adjustments in an NVP context. Several attempts have been made to quantify the outcomes of such adjustments. However, much of this literature assumes that accurate demand forecasts are available. We consider the (more realistic) case in which the forecasts may be inaccurate, due for example to insufficient data or model mis-specification. Computational results indicate that, in some cases, judgemental adjustment can lead to an increase in profit rather than a decrease. We discuss conditions under which the adjustments are beneficial and the situations when they are not. We also propose a heuristic algorithm for “tuning” the adjustment parameters in practice. In Chapter 5, we propose an alternative non-parametric approach to the variant of the NVP in which the goal is to minimise the conditional value at risk (CVaR). Given the difficulties with treating observations with extreme values, the existing parametric methods often underestimate the downside risk and lead to a significant loss in extreme cases. The existing non-parametric methods, on the other hand, are extremely computationally expensive with large instances and depend heavily on the form of the profit function. Using both simulation and real-life case studies, we show that our proposed method can be very useful in practice, allowing decisionmakers to suffer far less downside loss in extreme cases while requiring reasonable computing effort.